Static routes that point to an interface on a connected router will be advertised by way of Routing Information Protocol (RIP) and EIGRP regardless of whether redistribute static commands are specified for those routing protocols.

This situation occurs because static routes that point to an interface are considered in the routing table to be connected and hence lose their static nature. Also, the target of the static route should be included in the network (DHCP)command. If this condition is not met, no dynamic routing protocol will advertise the route unless a redistribute static command is specified for these protocols

The following is also good to know, I’ve noticed it’s source of common misunderstanding:

Specifying a numerical next hop that is on a directly connected interface will prevent the router from using proxy ARP. However, if the interface with the next hop goes down and the numerical next hop can be reached through a recursive route, you may specify both the next hop and interface (for example, ip route0.0.0.0 0.0.0.0 ethernet 1/2 10.1.2.3) with a static route to prevent routes from passing through an unintended interface.